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In this paper, we discuss several aspects of a potential new medical imaging modality for producing a quantitative three-dimensional map of neuron current densities associated with brain function. The neuromagnetic image is produced by reconstructing a current dipole field from external magnetic field measurements made with an array of superconducting quantum interference device (SQUID) detectors. This field is produced by numerical inversion of the Biot-Savart equation. The purpose of the work is to investigate fundamental limits on the feasibility of the proposed system under ideal conditions. The following problems are addressed: 1) What are the factors limiting resolution of the system? 2) What is a suitable model for neural activity in the brain? 3) What classes of algorithms are suitable for estimating the model parameters? The major conclusion of this work is that the inversion problem is severely ill-posed and the choice of model and estimation algorithm are crucial in obtaining reasonable solutions. A class of solutions, termed minimum dipole, is proposed as a means of obtaining more acceptable results.